Long multiplication is the standard algorithm for multiplying multi-digit numbers. It breaks down the multiplication into partial products based on place value, then adds them together.

Steps:

1. Write the larger number on top (multiplicand) and smaller below (multiplier)
2. Multiply the multiplicand by each digit of the multiplier, starting from the right
3. For each digit, place the result in the correct position (ones, tens, hundreds, etc.)
4. Add zeros to the right for place value (tens place = 1 zero, hundreds = 2 zeros, etc.)
5. Add all partial products together to get the final answer

Example: 234 × 56

Partial Products Explained:

• First partial product: 234 × 6 = 1404
• Second partial product: 234 × 5 (in tens place) = 1170, add one zero = 11700
• Final sum: 1404 + 11700 = 13104

Why it works: Long multiplication uses the distributive property: 234 × 56 = 234 × (50 + 6) = 234 × 50 + 234 × 6